Classification and numerical simulation of electric circuits. Kampowsky, W., Rentrop, P., & Schmidt, W. Surveys on Mathematics for Industry, 2(1):23–65, 1992.
Summary: In most electric circuit simulation packages the modified nodal voltage analysis is the basis for the mathematical modelling. In general, this approach leads to a system of implicit ordinary differential equations, which are generated automatically by a software package. Unfortunately, these equations are not given in symbolic form but exist only in evaluated form at discrete time steps. On the other hand, an implicit differential equation introduces new theoretical and numerical problems like the index or the requirement of consistent initial values. This is only partly reflected in actual implementations. We demonstrate these difficulties for several electric circuits, which have been modelled in symbolic form. Additionally we present a strategy for the computation of a stable periodic solution of an oscillator. The limit cycle is obtained from a two-point boundary value problem, which is solved by multiple shooting techniques. The presented circuits give the user of a simulation package more insight into the numerical performance and perhaps stimulate further numerical research for the specific needs of electric circuit simulation.
@Article{         Kampowsky_1992aa,
abstract      = {Summary: In most electric circuit simulation packages the modified nodal voltage analysis is the basis for the mathematical modelling. In general, this approach leads to a system of implicit ordinary differential equations, which are generated automatically by a software package. Unfortunately, these equations are not given in symbolic form but exist only in evaluated form at discrete time steps. On the other hand, an implicit differential equation introduces new theoretical and numerical problems like the index or the requirement of consistent initial values. This is only partly reflected in actual implementations. We demonstrate these difficulties for several electric circuits, which have been modelled in symbolic form. Additionally we present a strategy for the computation of a stable periodic solution of an oscillator. The limit cycle is obtained from a two-point boundary value problem, which is solved by multiple shooting techniques. The presented circuits give the user of a simulation package more insight into the numerical performance and perhaps stimulate further numerical research for the specific needs of electric circuit simulation. },
author        = {Kampowsky, Wilfried and Rentrop, Peter and Schmidt, Walter},
file          = {Kampowsky_1992aa.pdf},
journal       = {Surveys on Mathematics for Industry},
keywords      = {circuit,numerics},
langid        = {english},
number        = {1},
pages         = {23--65},
title         = {Classification and numerical simulation of electric circuits},
volume        = {2},
year          = {1992},
shortjournal  = {Surv. Math. Ind.}
}